Use Two Phase simplex procedure to solve it. An oil refinery has two sources of

Question

Use Two Phase simplex procedure to solve it.

An oil refinery has two sources of crude oil: a light crude that costs $ 35/barrel and a heavy crude that costs $ 30/barrel. The refinery produces gasoline, heating oil, and jet fuel from crude in the amounts per barrel indicated in the following table: The refinery has contracted to supply 900,000 barrels of gasoline, 800,000 barrels of heating oil, and 500,000 barrels of jet fuel. The refinery wishes to find the amounts of light and heavy crude to purchase so as to be able to meet its obligations at minimum cost. Formulate this problem as a linear program.

Explanation / Answer

Answer:

Let us assume that the refinery produce x barrel of light crude and y barrel of heavy crude.

Therefore our objective function is:

Minimize Z = 35x + 30y

and the constraints are:

0.3x + 0.3y <= 900000

0.2x + 0.4y <= 800000

0.3x + 0.2y <= 500000

Now add slack variables in the constraints (S1 and S2)

0.3x + 0.3y + S1 <= 900000

0.2x + 0.4y + S2 <= 800000

put x=y=0

S1 = 900000

S2 = 800000

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